Polynomial Averages Converge to the Product of Integrals

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dc.creatorFrantzikinakis, Nikos
dc.creatorKra, Bryna
dc.date2004-03-26
dc.date.accessioned2026-07-07T05:06:46Z
dc.date.available2026-07-07T05:06:46Z
dc.descriptionWe answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials of pairwise differing degrees, converges in $L^{2}$ to the product of the integrals. Such averages are characterized by nilsystems and so we reduce the problem to one of uniform distribution of polynomial sequences on nilmanifolds.
dc.description37A30
dc.identifierhttps://arxiv.org/abs/math/0403454
dc.identifierhttp://arxiv.org/abs/math/0403454
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70602
dc.subjectDynamical Systems
dc.titlePolynomial Averages Converge to the Product of Integrals
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